Strong Energy Condition in $R + R^2$ Gravity

J. H. Kung

doi:10.1103/PhysRevD.53.3017

paper

Strong Energy Condition in $R + R^{2}$ Gravity

arXiv:gr-qc/9510008 · doi:10.1103/PhysRevD.53.3017

Abstract

In this paper, we study Raychaudhuri's equation in the background of $R + β R^{2}$ gravity with a phenomenological matter ( $ρ \propto a (t)^{- n}$ ). We conclude that even though the Strong Energy Condition (S.E.C.) for Einstein's gravity, which guarantees singularity, is $n \geq 2$ for $ρ \propto a (t)^{- n}$ , a perturbative analysis of Raychaudhuri's equation in the background of $R + β R^{2}$ gravity reveals that the big bang singularity may not be guaranteed for $n > 4$ . We derive the following Strong Energy Conditions for $R + β R^{2}$ ( $β \neq = 0$ ): 1) For $k < 0$ FRW metric, S.E.C. is ( $0 \leq n \leq 4$ ) i.e., $- ρ_{n} \leq p_{n} \leq \frac{1}{3} ρ_{n}$ . 2) For $k = 0$ FRW metric, S.E.C. is ( $1 \leq n \leq 4$ ) i.e., $- \frac{2}{3} ρ_{n} \leq p_{n} \leq \frac{1}{3} ρ_{n}$ . 3) For $k > 0$ FRW metric, S.E.C. is ( $2 \leq n \leq 4$ ) i.e., $- \frac{1}{3} ρ_{n} \leq p_{n} \leq \frac{1}{3} ρ_{n}$ .

Submitted to Phy. Rev. D.,15 pages, 2 figures, Latex file

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Abstract

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Strong Energy Condition in $R + R^{2}$ Gravity